On the knapsack closure of 0-1 integer linear programs

Many inequalities for Mixed-Integer Linear Programs (MILPs) or pure Integer Linear Programs (ILPs) are derived from the Gomory corner relaxation, where all the nonbinding constraints at an optimal LP vertex are relaxed. Computational results show that the corner relaxation gives a good approximation of the integer hull for problems with general-integer variables, but the approximation is less satisfactory for problems with 0-1 variables only. A possible explanation is that, for 0-1 ILPs, even the non-binding variable bound constraints xj≥0 or xj≤1 play an important role, hence their relaxation produces weaker bounds.In this note we address a relaxation for 0-1 ILPs that explicitly takes all variable bound constraints into account. More specifically, we introduce the concept of knapsack closure as a tightening of the classical Chvátal-Gomory (CG) closure. The knapsack closure is obtained as follows: for all inequalities wTx≥w0 valid for the LP relaxation, add to the original system all the valid inequalities for the knapsack polytope conv{xε{0,1}n:wTx≥w0}. A MILP model for the corresponding separation problem is also introduced. © 2010 Elsevier B.V

The career of Maclyn McCarty

On January 2, 2005, the scientific community lost a valued colleague and friend. Maclyn McCarty, or “Mac,” as he was better known, was perhaps most recognized for his part in the discovery of DNA as the carrier of genetic information. But McCarty's scientific career was long and fruitful, and his contributions to science were vast. This retrospective offers a look at some of Mac's other notable scientific achievements

Branching on multi-aggregated variables

open5siopenGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, DomenicoGamrath, Gerald; Melchiori, Anna; Berthold, Timo; Gleixner, Ambros M.; Salvagnin, Domenic

The new Dutch timetable: The OR revolution

In December 2006, Netherlands Railways introduced a completely new timetable. Its objective was to facilitate the growth of passenger and freight transport on a highly utilized railway network, and improve the robustness of the timetable resulting in less train delays in the operation. Further adjusting the existing timetable constructed in 1970 was not option anymore, because further growth would then require significant investments in the rail infrastructure. Constructing a railway timetable from scratch for about 5,500 daily trains was a complex problem. To support this process, we generated several timetables using sophisticated operations research techniques, and finally selected and implemented one of these timetables. Furthermore, because rolling-stock and crew costs are principal components of the cost of a passenger railway operator, we used innovative operations research tools to devise efficient schedules for these two resources. The new resource schedules and the increased number of passengers resulted in an additional annual profit of 40 million euros ($60 million) of which about 10 million euros were created by additional revenues. We expect this to increase to 70 million euros ($105 million) annually in the coming years. However, the benefits of the new timetable for the Dutch society as a whole are much greater: more trains are transporting more passengers on the same railway infrastructure, and these trains are arriving and departing on schedule more than they ever have in the past. In addition, the rail transport system will be able to handle future transportation demand growth and thus allow cities to remain accessible. Therefore, people can switch from car transport to rail transport, which will reduce the emission of greenhouse gases.

PEGylating a bacteriophage endolysin inhibits its bactericidal activity

Bacteriophage endolysins (lysins) bind to a cell wall substrate and cleave peptidoglycan, resulting in hypotonic lysis of the phage-infected bacteria. When purified lysins are added externally to Gram-positive bacteria they mediate rapid death by the same mechanism. For this reason, novel therapeutic strategies have been developed using such enzybiotics. However, like other proteins introduced into mammalian organisms, they are quickly cleared from systemic circulation. PEGylation has been used successfully to increase the in vivo half-life of many biological molecules and was therefore applied to Cpl-1, a lysin specific for S. pneumoniae. Cysteine-specific PEGylation with either PEG 10K or 40K was achieved on Cpl-1 mutants, each containing an additional cysteine residue at different locations To the best of our knowledge, this is the first report of the PEGylation of bacteriophage lysin. Compared to the native enzyme, none of the PEGylated conjugates retained significant in vitro anti-pneumococcal lytic activity that would have justified further in vivo studies. Since the anti-microbial activity of the mutant enzymes used in this study was not affected by the introduction of the cysteine residue, our results implied that the presence of the PEG molecule was responsible for the inhibition. As most endolysins exhibit a similar modular structure, we believe that our work emphasizes the inability to improve the in vivo half-life of this class of enzybiotics using a cysteine-specific PEGylation strategy